PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
8001(22*10^64326+161)/364327Robert Price02/2017
800211^61767-405064324Enzo Doria12/2012
80032^213645-11485364314Enzo Doria05/2015
800413^57733+1864312Lelio R Paula07/2013
80052^213621+7270764307Enzo Doria04/2016
800610^64305+13679164306Patrick De Geest05/2011
800710^64305-964305Alexander Gramolin01/2011
8008V(307652)64295Serge Batalov03/2015
80094*10^64286-8964287Robert Price08/2017
8010(2^213546-5)/222164281Lelio R Paula04/2012
80112^213438-5869564252Lelio R Paula10/2011
80122^213367-10564230Lelio R Paula08/2011
8013595^23148+23148^59564225Norbert Schneider07/2016
80143^134601+868064221Lelio R Paula05/2013
8015(26*10^64220+61)/364221Robert Price06/2017
8016500^23793+23793^50064217Norbert Schneider08/2016
8017179^28504-264216Lelio R Paula10/2017
80192^213314-45564214Yves Minet02/2012
801839^40359-3864214Norbert Schneider05/2014
80202^213292-1608564208Enzo Doria04/2013
8021(72524!5+1)/2564203Joe McLean10/2018
80222^213274-7764202Lelio R Paula08/2011
802319^50203+7864198Lelio R Paula08/2013
8024(44*10^64192-233)/964193Robert Price10/2017
80252^213240-11286564192Enzo Doria06/2014
80262^213190-11239164177Enzo Doria06/2014
8027(9913*2^213184-1)/965764175Lelio R Paula04/2015
802814^55991+2764173Lelio R Paula07/2013
80292^213158-11258164167Enzo Doria06/2014
80302^213148+9164164Lelio R Paula08/2011
8031(96^32369+1)/9764163Paul Bourdelais08/2017
80336^82439+12564151Lelio R Paula07/2013
80327*2^213102+964151Lelio R Paula04/2014
8034L(306854)+F(306855)64129Henri Lifchitz01/2007
8035610^23017+23017^61064110Norbert Schneider07/2016
80362^212950-6487564105Lelio R Paula10/2011
8037(266*10^64102-17)/364104Robert Price06/2016
8038p(13679)#/2+6464097Robert Price03/2017
803919^50119+9464090Lelio R Paula08/2013
80402^212880-14764084Lelio R Paula08/2011
804111^61523-459064070Enzo Doria01/2013
80425^91663+3864070Lelio R Paula05/2013
80435^91650+5264061Lelio R Paula05/2013
80442^212770+6964051Lelio R Paula08/2011
8045(3^134227+1)/464042Paul Bourdelais11/2007
8046(2*10^64041-17)/364041Robert Price08/2014
8047(15^54449+1)/1664036Paul Bourdelais03/2010
8048(29*10^64027+91)/364028Robert Price03/2016
8049(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
805016878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
80512^212663+5364018Lelio R Paula08/2011
8052(4*10^64014+197)/364015Robert Price03/2017
805385402!6-364014Robert Price08/2018
8054(140^29819+1)/14163994Richard Fischer05/2018
805510^63986+6363987Robert Price01/2011
805610^63986-3155763986Patrick De Geest05/2013
805731487!2-2^3148763982Robert Price09/2015
8058(21*2^212522-1)/141632363971Lelio R Paula01/2014
80595^91517+9863968Lelio R Paula04/2013
8060(19*10^63960-43)/363961Robert Price10/2017
8061(62*10^63954-17)/963955Robert Price09/2015
80635^91493-4^9149363951Predrag Minovic04/2004
8062V(364793)63951Serge Batalov03/2015
806519^50004+5863943Lelio R Paula05/2013
80645*6^82172-763943Lelio R Paula09/2014
8066(56*10^63942+223)/963943Robert Price07/2016
806719^50000-2463938Lelio R Paula05/2013
8068(23*2^212374-1)/2701963928Lelio R Paula01/2014
8069(9*2^212355-1)/76163924Lelio R Paula01/2014
80712^212344-18363922Lelio R Paula08/2011
8070(58695*2^212336-1)/37963922Lelio R Paula04/2015
807210^63916+7963917Robert Price01/2011
807310^63916-7682363916Patrick De Geest05/2013
80742^212295-2563908Lelio R Paula08/2011
80762^212285-238363905Yves Minet10/2013
8075267^26336+26336^26763905Norbert Schneider09/2014
8077(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
807819^49962+6063890Lelio R Paula05/2013
80793^133906-11305663890Enzo Doria07/2014
8080(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
80813*6^82092+563881Lelio R Paula09/2014
808215441^13706+13706^1544163879Hans Havermann02/2017
80832^212154-77635163865Paul Bourdelais03/2013
808435^41359+263862Lelio R Paula05/2013
8085(61*10^63857-43)/963858Robert Price09/2015
8086(2^212131-3)/48563856Lelio R Paula04/2012
80872^212112-45999563853Enzo Doria06/2015
808815^54290+5863850Lelio R Paula05/2013
80893*2^212097-763849Lelio R Paula04/2014
809055^36683-5463842Norbert Schneider08/2014
8091(509203*2^212056-1)/363841Lelio R Paula04/2015
8092(3^133805-7)/17263839Lelio R Paula04/2012
80932^212049+14963834Lelio R Paula08/2011
80945^91318-1863829Lelio R Paula04/2013
809518468^2857+2857^1846863824Hans Havermann03/2017
8096(2^212024-5)/111163823Lelio R Paula04/2012
80972^211961+1291563807Lelio R Paula02/2013
8099(3^133707-7)/578063791Lelio R Paula04/2012
8098(44*10^63790-161)/963791Robert Price11/2017
8100747^22198+22198^74763782Norbert Schneider07/2016
81012^211800-1716963759Enzo Doria05/2013
8102(85*10^63757-1)/363759Robert Price07/2017
810385089!6-863757Robert Price08/2018
8104(14*10^63747-11)/363748Erik Branger09/2014
810591*19^49848+663746Curtis Bright05/2015
810618855^2402+2402^1885563741Hans Havermann03/2017
8107(142*10^63734-7)/963736Robert Price02/2017
81082^211699-11163728Lelio R Paula08/2011
810911^61192-555063725Enzo Doria01/2013
8110(11*10^63718+7)/963719Serge Batalov06/2011
81116^81872-1363709Lelio R Paula04/2013
81123^133522+9863707Lelio R Paula05/2013
81142^211607-6163701Lelio R Paula08/2011
81135^91135+863701Lelio R Paula04/2013
811511^61157-27063689Enzo Doria07/2012
811710^63685+114514191963686Marisa Kirisame03/2015
811610^63685+10383763686Patrick De Geest03/2016
811810^63685-13079763685Patrick De Geest03/2016
81192^211547+1155*21154763682Henri Lifchitz02/2005
81202^211543+4563681Lelio R Paula08/2011
81212^211534+4363679Lelio R Paula08/2011
812211^61140-6063671Enzo Doria07/2012
81232^211491-11232163666Enzo Doria06/2014
812419085^2164+2164^1908563654Hans Havermann03/2017
8125(2^211430-5)/85963644Lelio R Paula04/2012
81262^211401-9163639Lelio R Paula08/2011
8127(6883*2^211378-1)/6963634Lelio R Paula04/2015
8128(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
8129(29*2^211384-1)/5012262163627Lelio R Paula01/2014
81302^211333+1501563618Lelio R Paula01/2013
813133^41889-3263610Norbert Schneider03/2014
813213^57093+1863599Lelio R Paula05/2013
8133(5*2^211219-1)/963583Lelio R Paula01/2014
8134(107*10^63576-17)/963578Robert Price02/2017
813523^46687-102063575Enzo Doria08/2012
8136(67607*2^211188+1)/523431963573Lelio R Paula06/2014
8137(3^133243+7)/1072663570Lelio R Paula04/2012
8138(7*2^211181+1)/274563570Lelio R Paula06/2012
8140(20^48859-1)/1963566Paul Bourdelais03/2010
81392*3^133227+563566Lelio R Paula04/2014
81412^211155+11363564Lelio R Paula08/2011
81422^211134+34563558Lelio R Paula09/2011
81432^211121+1638563554Lelio R Paula09/2011
814416996^5483+5483^1699663549Hans Havermann02/2017
8145(2^211079+9)/36428363536Lelio R Paula03/2012
81463*10^63522+1363523Robert Price08/2017
814715852^10157+10157^1585263516Hans Havermann02/2017
81482^210948-1587363502Enzo Doria04/2013
81497^75136+663498Lelio R Paula04/2013
81502^210928+1291563496Lelio R Paula02/2013
81517*10^63493+3963494Robert Price07/2016
81522^210909+13563490Lelio R Paula08/2011
8153(3*2^210832+1)/763467Lelio R Paula07/2012
81548*7^75098-363467Lelio R Paula09/2014
815517683^3882+3882^1768363466Hans Havermann03/2017
8157Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
81562^210820-1690563464Enzo Doria05/2013
81585^90795-3663463Lelio R Paula04/2013
815984731!6-4863463Robert Price08/2018
81602^210816-1319763462Enzo Doria10/2012
81612^210750+13363443Lelio R Paula08/2011
8162291^25742+25742^29163426Norbert Schneider09/2014
8163(3^132908+8)/27985963408Lelio R Paula04/2012
81646^81480-13963404Lelio R Paula04/2013
81652^210576-17363390Lelio R Paula08/2011
816618^50497+5563388Lelio R Paula05/2013
81672^210545+1163381Lelio R Paula08/2011
81682^210543+6363380Lelio R Paula08/2011
8169155^28929-15463365Norbert Schneider12/2018
817083^33016+8263361Norbert Schneider04/2015
81712^210464+9876533163356Jason Earls12/2008
81727*10^63351+963352Dmitry Domanov11/2010
8173p(13534)#/2+51263348Robert Price05/2017
81741741^19546+19546^174163345Serge Batalov05/2014
817510^63336+1981963337Patrick De Geest12/2013
817610^63336-12288363336Patrick De Geest12/2013
8177(19^49523-2^49523)/1763327Robert Price09/2013
8178(2^210378+47)/9551693163323Lelio R Paula03/2012
817931191!2+25663316Robert Price01/2015
818016458^7031+7031^1645863315Hans Havermann01/2017
8181(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
8182156^28864+15563303Norbert Schneider12/2018
8183(2^210283+7)/169114563296Lelio R Paula03/2012
81842^210217+129963282Lelio R Paula09/2011
8185(2^210221-3)/26963281Lelio R Paula04/2012
8186Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
818796^31913-9563261Norbert Schneider04/2016
81883^132572+28063253Lelio R Paula04/2013
81893^132570-2^(132570-1)63252Robert Price01/2016
819011^60734-492063248Enzo Doria01/2013
81922^210061+2163235Donovan Johnson06/2006
819118^50375+9563235Lelio R Paula05/2013
819385^32773-263233Lelio R Paula08/2013
8194(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
8195(2^210054-1017)/67163230Lelio R Paula04/2012
81963*2^210022+563224Lelio R Paula04/2014
819715^53756+3263222Lelio R Paula05/2013
819817^51380+2263221Lelio R Paula05/2013
8199(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
820043^38700+4263216Norbert Schneider06/2014
82015^90431-9663209Lelio R Paula04/2013
8202(172*10^63202-1)/963204Serge Batalov12/2014
8203(43*10^63200+83)/963201Robert Price08/2017
82042^209914-1600563191Enzo Doria04/2013
82053*6^81190-563179Lelio R Paula09/2014
82062^209820+425763163Lelio R Paula10/2011
820799^31648+263158Lelio R Paula05/2013
820816976^5253+5253^1697663158Hans Havermann01/2017
82092^209790+6763154Lelio R Paula08/2011
8210145878#-p(145878)63152Henri Lifchitz12/2018
82112^209759+9019563144Lelio R Paula02/2013
8212145823#+21150763142Arkadiusz Wesolowski03/2013
82132^209707+51363129Lelio R Paula10/2011
8214(3^132314-8)/1763129Lelio R Paula04/2012
8215(2*10^63117+7)/963117Erik Branger03/2011
82169*2^209654-763114Lelio R Paula04/2014
821784304!6-963112Robert Price08/2018
821811^60598-1463107Lelio R Paula05/2013
821915103^15078+15078^1510363106Hans Havermann01/2017
822015346^12941+12941^1534663103Hans Havermann01/2017
82213^132253+7663101Lelio R Paula04/2013
8222(56*10^63100+403)/963101Robert Price10/2017
822317549^3936+3936^1754963090Hans Havermann01/2017
8224(55459*2^209553+1)/42363084Lelio R Paula06/2014
8225(331^25033-1)/33063077Eric Chen09/2017
822720^48480+3163074Lelio R Paula06/2013
8226(26*10^63073-23)/363074Robert Price08/2016
82282^209499+7625363066Enzo Doria04/2016
822911^60546-1134063053Enzo Doria12/2012
82302^209426+5788963044Yves Minet02/2010
8231(22699*2^209405+1)/2163041Lelio R Paula06/2014
82325^90189+5463040Lelio R Paula04/2013
8233(22*10^63034-73)/363035Robert Price09/2017
8234(314021^11467+1)/31402263029Faysal YAtim05/2008
8235V(301486)63007Henri Lifchitz05/2003
8236(31*2^209298+1)/9563005Lelio R Paula08/2012
8237(27*2^209245+1)/562990Lelio R Paula08/2012
82386^80946-5^(80946-1)62989Robert Price05/2016
8239467^23596+23596^46762986Norbert Schneider08/2016
8240(7*2^209212-1)/362980Lelio R Paula01/2014
8241(27*2^209206-1)/1162978Lelio R Paula01/2014
82421456^19909+19909^145662976Serge Batalov05/2014
8243(3^131964-5)/18521239662955Lelio R Paula04/2012
824435^40772-146662955Enzo Doria03/2013
82455^90064-1370662953Enzo Doria02/2013
8246(22*10^62926+257)/962927Robert Price11/2017
8247(13*10^62914+401)/962915Robert Price10/2017
82482^208993+10762914Lelio R Paula08/2011
82492^208993+7762914Lelio R Paula08/2011
8250189^27636-262913Lelio R Paula10/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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